1. Field of the Invention
The present invention relates to a piezoelectric resonator and a piezoelectric filter including the same, and more particularly, for example, to a piezoelectric resonator that generates a thickness longitudinal vibration or a thickness-shear vibration and to a piezoelectric filter including a plurality of piezoelectric resonators.
2. Description of the Related Art
As a piezoelectric resonator using a thickness longitudinal vibration fundamental wave, for example, a piezoelectric resonator shown in FIGS. 1A and 1B has been reported (K. NAKAMURA, H. SASAKI, H. SHIMIZU: Faculty of Engineering, Tohoku University xe2x80x9cZnO/SiO2-DIAPHRAGM COMPOSITE RESONATOR ON A SILICON WAFERxe2x80x9d, ELECTRONICS LETTERS, Jul. 9th, 1981, Vol.17, No.14). In this piezoelectric resonator 1, an SiO2 layer having a thickness of 2.5 xcexcm defines a dielectric layer 2, and a ZnO layer having a thickness of 4.5 xcexcm defines a piezoelectric layer 3. Then, on both surfaces of the piezoelectric layer 3, a pair of opposing electrode layers 4a and 4b are disposed. The portion where the electrode layers 4a and 4b oppose each other has a rectangular planar shape having dimensions of 350 xcexcmxc3x97140 xcexcm.
The resonance characteristic of such a piezoelectric resonator 1 is shown in FIG. 2. In FIG. 2, the largest response is the resonance of a longitudinal vibration fundamental wave, which is called an S0 mode and is a desired resonance (main vibration). Small responses are generated at the high-frequency side of this main vibration, and are called S1, S2, S3, . . . mode in order of closeness to the main vibration. These modes are resonances (spurious vibrations) that, preferably, should not exist in the characteristic. The nature of these spurious vibrations is such that the states change according to the diameters of the electrodes, and as the diameters of the electrodes become large, the responses become large, and the responses come close to the main vibration. Accordingly, conventionally, in order to prevent the influence of the spurious vibrations, the radius of the electrodes is decreased enough to isolate the spurious vibrations from the main vibration, and the responses thereof are decreased.
However, the diameters of the electrodes affect not only the spurious vibrations but also the main vibration. When the diameters of the electrodes are small, since the area of the electrodes is decreased, the impedance of the resonator is increased, and the response of the main vibration is decreased. As described above, the spurious vibrations of the resonator and the impedance have a trade-off relationship. Therefore, the problem is that, if one of the spurious vibrations and the impedance is improved, the other is worsened.
For example, if the diameters of the electrodes is decreased until the spurious vibrations are small enough to use the resonator for an oscillator, the spurious vibrations disappear, and although the oscillation frequency may not move to the spurious vibrations for some reason, an increase in impedance of the resonator does not cause oscillation. On the other hand, if the radius of the electrodes is increased to produce an impedance that allows for oscillation, the spurious vibrations move closer to the main vibration, since the response thereof becomes large, and a problem occurs that the spurious vibrations oscillate and the oscillation frequency is not stable.
Also, in a ladder-type filter in which such piezoelectric resonators are combined, in relation to the trade-off of the impedance and spurious vibrations, if the diameters of the electrodes are decreased to suppress the spurious vibrations, since the impedance of the resonator cannot be reduced enough and the response of the main vibrations cannot be increased, there is a problem in that the insertion loss becomes large with respect to the characteristic of the ladder-type filter and the pass-band cannot be widened. On the other hand, if the diameters of the electrodes are increased, the spurious vibrations approach the main vibrations and interfere therewith. Accordingly, in the ladder-type filter in which these piezoelectric resonators are combined, a problem occurs in that a large ripple is produced in the pass-band.
In order to solve the problems described above, preferred embodiments of the present invention provide a piezoelectric resonator which has a small impedance and is hardly affected by the spurious vibrations.
In addition, preferred embodiments of the present invention provide a piezoelectric filter in which a ripple that occurs due to the influence of the spurious vibrations of the piezoelectric resonator in a pass band is minimized, while the filter has a wide pass band.
According to a preferred embodiment of the present invention, a piezoelectric resonator using an nth-order mode of a thickness longitudinal vibration or a thickness-shear vibration includes a vibrating section having a piezoelectric layer, a pair of electrodes and a support member for holding the vibrating section. The pair of electrodes are provided on opposite sides of the piezoelectric layer, respectively, and the pair of electrodes partially overlap with each other via the piezoelectric layer to define an opposite electrode portion. The support member holds the vibrating section such that the vibrating section vibrates in an nth-order mode of a thickness longitudinal vibration or a thickness-shear vibration. The opposite electrode portion preferably has a substantially circular shape having a radius r or preferably has a polygonal shape that circumscribes the substantially circular shape, and the radius r satisfies the following inequality:
20t/nxe2x89xa6r
where t is a thickness of the vibrating section.
A mechanical quality coefficient of the piezoelectric resonator is preferably about 1000 or more, and the radius r of substantially circular shape preferably satisfies the inequality 40t/nxe2x89xa6r. Alternatively, the mechanical quality coefficient of the piezoelectric resonator may be less than about 1000, and the radius r of the substantially circular shape satisfies the inequality 20t/nxe2x89xa6r less than 40.
The vibrating section may further include a dielectric layer, and temperature coefficients of elastic constant of the piezoelectric layer and the dielectric layer may have polarities that are different from each other. Alternatively the vibrating section may include another piezoelectric layer, and temperature coefficients of elastic constant of the two piezoelectric layers may have different polarities from each other.
In a piezoelectric resonator in which opposing electrodes are disposed in a piezoelectric body, it is known that the smaller r/t is, the farther the main vibration moves away from the spurious vibration, and the larger the ratio r/t is, the more the spurious vibration comes closer to the main vibration, wherein the radius of a substantially circular electrode is r, the thickness of a vibrating section is t. Conventionally, the spurious vibrations are kept away from the spurious vibration by decreasing the diameter of the electrode. In the present invention, the spurious vibrations are concentrated around the main vibration by increasing the diameter of the electrode enough in order to surely resonate in the frequency of the main vibrations.
The impedance can be minimized and made to be very small by increasing the diameter of the electrode. Furthermore, since the spurious vibrations concentrate around the main vibration, the resonator can surely resonate in the frequency of the main vibration. To obtain this effect, the radius r of the electrode is preferably within the range of rxe2x89xa720t/n, wherein the thickness of the vibrating section is t and when an nth-order mode is used.
Regarding the range of the radius r of the electrode, especially when a mechanical quality coefficient Qm is about 1000 or more, it is rxe2x89xa740t/n, and when the mechanical quality coefficient Qm is less than about 1000, it is rxe2x89xa720t/n.
When the vibration section includes a composite structure of the piezoelectric body and the dielectric body or a composite structure of a plurality of piezoelectric bodies, in the relationship between one of the layers and the other layers, if a temperature coefficient of elastic constant is an inverted sign, by an appropriate combination, a change in frequency due to a change in temperature can be zero. Thus, a piezoelectric resonator that has a highly stable resonant frequency for the change in temperature and is hardly affected by the spurious vibration can be obtained.
When using a piezoelectric filter including a combination of a plurality of piezoelectric resonators, by using the piezoelectric resonators according to the above-described preferred embodiments of the present invention, a ripple generated in a pass band due to the spurious vibration can be suppressed. Also, by concentrating the spurious vibration of the piezoelectric resonator around the main vibration, these interfere with each other, and the difference xcex94f between the resonance frequency and the anti-resonant frequency is large, and a piezoelectric resonator having a wide pass band can be obtained.
Other features, elements, characteristics and advantages of the present invention will become more apparent from the following detailed description of preferred embodiments thereof with reference to the attached drawings.
For the purpose of illustrating the present invention, there is shown in the drawings several forms which are presently preferred, it being understood, however, that the invention is not limited to the precise arrangements and instrumentalities shown.